Related papers: Neuc-MDS: Non-Euclidean Multidimensional Scaling T…
The density based clustering method {\em Density-Based Spatial Clustering of Applications with Noise (DBSCAN)} is a popular method for outlier recognition and has received tremendous attention from many different areas. A major issue of the…
We propose a unified mixture sampler (UMS) that provides a universal estimation framework for nonlinear state-space models with "exp-exp" likelihood kernels. Unlike existing methods that require deriving new mixture approximations for each…
Existing distribution compression methods reduce the number of observations in a dataset by minimising the Maximum Mean Discrepancy (MMD) between original and compressed sets, but modern datasets are often large in both sample size and…
We extend the data-assimilation approach of Ling and Lozano-Dur\'an (AIAA 2025-1280) to develop machine-learning-based subgrid-scale stress (SGS) models for large-eddy simulation (LES) that are consistent with the numerical scheme of the…
This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…
Real-world data usually have high dimensionality and it is important to mitigate the curse of dimensionality. High-dimensional data are usually in a coherent structure and make the data in relatively small true degrees of freedom. There are…
A finite set of the Euclidean space is called an $s$-distance set provided the number of Euclidean distances in the set is $s$. Determining the largest possible $s$-distance set for the Euclidean space of a given dimension is challenging.…
Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…
A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…
In this paper, we introduce principal asymmetric least squares (PALS) as a unified framework for linear and nonlinear sufficient dimension reduction. Classical methods such as sliced inverse regression (Li, 1991) and principal support…
The classic Alternating Direction Method of Multipliers (ADMM) is a popular framework to solve linear-equality constrained problems. In this paper, we extend the ADMM naturally to nonlinear equality-constrained problems, called neADMM. The…
Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a…
Recent advances have markedly improved the cross-scene generalization of relative depth estimation, yet its practical applicability remains limited by the absence of metric scale, local inconsistencies, and low computational efficiency. To…
We present R and C implementations for metric (ratio) and non-metric (ordinal) versions of Elastic MDS, the multidimensional scaling technique proposed by McGee (1966). The R and C versions are compared for speed, with the C version…
We propose a ultraviolet complete theory for cold dark matter(CDM) and sterile neutrino that can accommodate both cosmological data and neutrino oscillation experiments at $1\sigma$ level. A new $U(1)_X$ dark gauge symmetry is introduced,…
There are many application papers that solve elliptic boundary value problems by meshless methods, and they use various forms of generalized stiffness matrices that approximate derivatives of functions from values at scattered nodes…
Deep-feature-based perceptual similarity models have demonstrated strong alignment with human visual perception in Image Quality Assessment (IQA). However, most existing approaches operate at a single spatial scale, implicitly assuming that…
Multi-dimensional scaling (MDS) plays a central role in data-exploration, dimensionality reduction and visualization. State-of-the-art MDS algorithms are not robust to outliers, yielding significant errors in the embedding even when only a…
Clustering procedures suitable for the analysis of very high-dimensional data are needed for many modern data sets. In model-based clustering, a method called high-dimensional data clustering (HDDC) uses a family of Gaussian mixture models…
Clustering methods are a valuable tool for the identification of patterns in high dimensional data with applications in many scientific problems. However, quantifying uncertainty in clustering is a challenging problem, particularly when…